Preheat a sauté pan and drizzle olive oil to cover the bottom, add onions and garlic, then reduce the heat to medium and cook until the onions turn translucent. Add peppers and season with salt and pepper, stir every couple of minutes to ensure an even cooking. Cook until the peppers are soft, but still a little crisp. Add the tomatoes, rosemary, thyme, olives and capers. Let the mixture simmer for 8 to 10 minutes, then turn off the heat and add the basil, lemon zest and juice.
Place all the salsa verde ingredients in a blender and purée on high speed into a thin green paste. Taste and adjust the seasoning with salt and pepper.
Let the steak rest on the counter one hour before cooking. Season with salt and pepper on both sides. Take a sprig of both rosemary and thyme, then press the herbs into the steak to make them stick to the meat.
Preheat a cast iron skillet over medium-high heat. Drizzle olive oil into pan, and when it starts to smoke, add the steak and sear for 5 minutes. When it develops a nice crust on one side, turn it over. Add 1 more sprig of rosemary, 2 sprigs of thyme and butter. Baste the steak with melted butter constantly. Cook for another 4 minutes or until it reaches your desired doneness. Let the steak rest on a cutting board for 5 minutes before slicing.